M16c The Symmetric Core: Spectral Theory, S-Duality, the Kneser Euler Product, and the RH Programme

This monograph develops the spectral theory of the Symmetric Core and formulates a disciplined SC Riemann Programme, independent of physical interpretation. Central constructions include the LP curve in the spectral parameter plane, zero‑migration equations, equivariant degeneracy results, and the formulation of a self‑adjoint SC candidate for a Hilbert–Pólya‑type operator. The RGSB framework organises spectral transport and constrains zero motion under rank deformation. The work reformulates classical zeta‑type objects in SC‑native coordinates, relates them to Kneser–Lerch families, and derives symmetry constraints leading to zero quadruplet structures. The monograph does not claim a proof of the Riemann Hypothesis; it provides a precise reduction of the problem to a small set of explicitly stated spectral conditions.